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Solvability of the Integro-Differential Equation in the Problem of Wave Diffraction on a Junction of Rectangular Waveguides

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Abstract

We study the problem of electromagnetic wave diffraction on a junction of two rectangular waveguides. The boundary value problem for the system of Maxwell equations is reduced to a vector pseudodifferential equation in special Sobolev spaces. Sufficient conditions are obtained for the existence of a unique solution of the boundary value problem and the integro-differential equation.

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REFERENCES

  1. Feynman, R.P., Leighton, R.B., and Sands, M., The Feynman Lectures in Physics. Vol. 2 , Reading, MA: Addison Wesley, 1964.

    Google Scholar 

  2. Smirnov, Yu.G., On solvability of vector diffraction problems in domains coupled via an aperture in the screen, Zh. Vychisl. Mat. Mat. Fiz., 1993, vol. 33, no. 9, pp. 1427–1440.

    MathSciNet  MATH  Google Scholar 

  3. Il’inskii, A.S. and Smirnov, Yu.G., Difraktsiya elektromagnitnykh voln na provodyashchikh tonkikh ekranakh (Diffraction of Electromagnetic Waves by Conducting Thin Screens), Moscow: Red. Zh. Radiotekhnika, 1996.

    Google Scholar 

  4. Ilyinsky, A.S. and Smirnov, Yu.G., Electromagnetic Wave Diffraction by Conducting Screens, Utrecht: VSP, 1998.

    Google Scholar 

  5. Smirnov, Yu.G., On the Fredholm property of the problem of diffraction by a planar bounded perfectly conducting screen, Dokl. Akad. Nauk SSSR, 1991, vol. 319, no. 1, pp. 147–149.

    Google Scholar 

  6. Smirnov, Yu.G., On the Fredholm property of the system of pseudodifferential equations in the problem of diffraction by a bounded screen, Differ. Uravn., 1992, vol. 28, no. 1, pp. 136–143.

    MathSciNet  MATH  Google Scholar 

  7. Smirnov, Yu.G., Solvability of integro-differential equations in the problem of diffraction by a perfectly conducting planar screen, Radiotekh. Elektron., 1992, vol. 37, no. 1, pp. 32–35.

    Google Scholar 

  8. Smirnov, Yu.G., On the solvability of vector integro-differential equations in the problem of diffraction of electromagnetic field by arbitrarily shaped screens, Zh. Vychisl. Mat. Mat. Fiz., 1994, vol. 34, no. 10, pp. 1461–1475.

    MathSciNet  Google Scholar 

  9. Smirnov, Yu.G., On the solvability of vector electrodynamic problems on nonclosed surfaces, Differ. Uravn., 1995, vol. 31, no. 11, pp. 1936–1937.

    Google Scholar 

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Funding

This work was supported by the Russian Foundation for Basic Research, project no. 19-31-51004.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, 119991, Russia

    A. S. Ilyinsky

  2. Penza State University, Penza, 440026, Russia

    Yu. G. Smirnov

  3. Sirius University, Sochi, Krasnodar krai, 354340, Russia

    Yu. G. Smirnov

Authors
  1. A. S. Ilyinsky
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  2. Yu. G. Smirnov
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Corresponding authors

Correspondence to A. S. Ilyinsky or Yu. G. Smirnov.

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Translated by V. Potapchouck

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Ilyinsky, A.S., Smirnov, Y.G. Solvability of the Integro-Differential Equation in the Problem of Wave Diffraction on a Junction of Rectangular Waveguides. Diff Equat 56, 1041–1049 (2020). https://doi.org/10.1134/S0012266120080078

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  • DOI: https://doi.org/10.1134/S0012266120080078

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